1. Field of the Invention
The recently published literature shows the need for a comprehensive integrated modeling solution for coupling multiple reservoir simulations and surface facility networks.1-8 This need is emphasized by recent deepwater oil and gas field development where, typically, wells from different reservoirs flow through pipelines to a shared surface facility platform before being transported by a pipeline to the sale point. Surface/subsurface coupling involves several issues including:                The coupling mode of the surface and subsurface models: explicit or implicit. This has previously been described for the case of a single reservoir simulation coupled to a surface network model.9,10         The application of global production and injection/re-injection constraints to a coupled system of multiple reservoirs.11         The use of different PVT models (black oil models and compositional models having different sets of pseudo-components) in the coupled reservoirs and the surface network model.4,5         Time step synchronisation and coupling scheme in the case of multiple coupled reservoirs.11         The surface/subsurface coupling location: whether to couple at the well head or at the reservoir level (with various degrees of overlapping).12         
2. Description of the Related Art
Litvak and Darlow7 and Litvak and Wang14 used an implicit compositional reservoir model/surface network coupling. In this mode, the equations describing multiphase fluid flow in the reservoir, the well inflow relationship, the well. tubing model and the surface facility model are solved simultaneously. Treating the wellheads and nodes of the surface pipelines equivalently to additional grid blocks of the reservoir model, the complete system of equations is linearized and the resulting linear system is solved to obtain the updated values of the solution variables at each Newton iteration.
Although an implicit: surface/subsurface coupling might provide better convergence when solving the non-linear system of equations, it suffers from a lack of flexibility when it comes to software choice.12 Furthermore, coupling several reservoir models to a shared surface facility is not feasible implicitly without amalgamating these models into a single grid (with a large number of grid blocks), which would be inefficient and difficult to maintain.11,13 
An alternative to implicit surface/subsurface coupling is an iteratively lagged scheme. At each Newton iteration of the reservoir model, the surface network is balanced with the well/reservoir model using the latest iterate of the reservoir solution. When a balanced solution has been obtained, it is applied as a control target to the wells in the reservoir model while the reservoir simulator performs its next Newton iteration of the solution. The control target may typically be the tubing head pressure (THP), the bottom hole pressure (BHP) or the flow rate of each well obtained from the balanced surface/subsurface solution.
The advantages of an iteratively lagged coupling scheme are its simplicity and flexibility. A fully implicit coupling scheme requires additional derivatives to be computed reflecting the coupling of the wells through the network, and these must be accommodated in the Jacobian matrix of the reservoir simulator. An iteratively lagged scheme omits these derivatives, reducing the data communication between the surface and subsurface models to the instantaneous conditions at the coupling points (e.g. well rates, pressure, PI). The scheme is therefore an appropriate choice for coupling independent surface and subsurface simulators; this solution can offer more flexibility in the choice of software, provided that each simulator has a compatible open interface through which they can exchange data.12 
The main disadvantage of an iteratively lagged scheme relative to a fully implicit scheme that includes all the derivatives is that the reservoir simulator may require more Newton iterations to converge its time step. Without the extra derivatives from the surface network model, the Jacobian matrix in the reservoir model does not take into account the response of the network to the changes in the well and reservoir solution over each Newton iteration. In some circumstances omitting these derivatives may compromise the convergence of the time step. The remedy is to balance the network with the well/reservoir model only in the first few Newton iterations of each time step (typically 2 or 3). If the reservoir simulator requires more Newton iterations than this to converge the time step, the well control targets are kept constant for the remainder of the time step calculation. This scheme has been used successfully for many years, for group control applications and for coupling integrated network models built into the reservoir simulator.
The iteratively lagged coupling scheme; however, is not well suited for cases where multiple reservoir models are coupled to the surface model. In general, the reservoir models will choose different time step sizes and will solve their time steps with different numbers of Newton iterations. An iteratively lagged coupling scheme would require the reservoir models to be tightly synchronised to take the same time steps (the minimum of the time step sizes of all the models), which may slow the simulation process considerably. An alternative coupling scheme for these cases is an explicit (‘loose’) coupling in which the reservoir models are synchronized at specific times chosen by the controller (the ‘controller time step’) and the network balancing is performed at the start of each controller time step. The reservoir models are then allowed to advance independently to the start of the next controller time step, taking as many of their own time steps as they deem necessary, while keeping their well control targets constant at the value set by the latest balanced network solution. This is less accurate than the iteratively lagged scheme and may result in a degree of inconsistency between the reservoir and network solutions. Issues and remedies related to explicit coupling are discussed later in this paper.
Several integrated modeling solutions have been reported that enable multiple reservoirs to be coupled to shared surface facilities.1,2,4,11 The most functionally advanced among these models is the Hydrocarbon Field Planning Tool (BFPT)4 in which multiple reservoir models (black oil or compositional) are coupled to a shared surface network. Surface/subsurface coupling takes place through an open interface and provides balanced pressures at the well tubing heads. Coupling a black oil reservoir model to a compositional surface network model is also allowed, using an advanced black oil delumping scheme.5 However, the referenced material regarding HFPT does not describe the technical details involved in a multiple reservoir/network coupling scheme.